How many ways to climb n numbers of stairs if you could climb them 1, 2, 3 flights at a time

stairs.py

"""
How many ways to climb n numbers of stairs if you could climb them 1, 2, 3
flights at a time
"""


def stairs(num):
    """
    This solution depends on how many ways I could get to any flight of staits.
    When I could reach a flight (i) with n ways and I could reach flight (i + 1)
    with (m) ways without passing by flight (i), then the total way of reaching
    flight (i + 1) is (n + m)

    Time complexity = O(n)
    Space complexity = O(n)

    """
    # Rejecting any number of flights if its <= 0
    if num <= 0:
        return 0
    # Initializing a list. List[0] is before taking any steps
    steps, moves = [0 for i in range(num + 1)], [1, 2, 3]
    for i in range(0, num):
        ways = max(1, steps[i])
        for m in moves:
            if i + m <= num:
                steps[i + m] += ways
    return steps[num]